Special precision bolts are made by another machine. These are for jobs that require more exact measurements. The bolts must be
within 0.01 mm of 8 mm. This is represented by |x – 8| < 0.01.
Write this inequality as a compound inequality without absolute value bars.
Solve the inequality.
Graph the solutions on a number line.
What do the solutions of the inequality mean for the bolt?
Write this inequality as a compound inequality without absolute value bars.
Solve the inequality.
Graph the solutions on a number line.
What do the solutions of the inequality mean for the bolt?
1 answer:
Answer:
-.01 < x-8 < .01
7.99 < x< 8.01
see attached
The bolts must be greater than 7.99mm and less than 8.01 mm
Step-by-step explanation:
|x – 8| < 0.01
to remove the absolute value bars, we need the positive and negative solutions
x-8 < .01 and x-8 > -.01
-.01 < x-8 < .01
solve
add 8 to each side
-.01 < x-8 < .01
8 + -.01 < x-8+8 < .01 +8
7.99 < x< 8.01
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Answer:
9.34%
Step-by-step explanation:
p = 4%, or 0.04
n = Sample size = 667
u = Expected value = n * p = 667 * 0.04 = 26.68
SD = Standard deviation = = 5.06
Now, the question is if the manager is correct, what is the probability that the proportion of flops in a sample of 667 released films would be greater than 5%?
This statement implies that the p-vlaue of Z when X = 5% * 667 = 33.35
Since,
Z = (X - u) / SD
We have;
Z = (33.35 - 26.68) / 5.06
Z = 1.32
From the Z-table, the p-value of 1.32 is 0.9066
1 - 0.9066 = 0.0934, or 9.34%
Therefore, the probability that the proportion of flops in a sample of 667 released films would be greater than 5% is 9.34%.